Praise be to Allaah.
Menses does not prevent a woman from entering ihraam for Hajj and ‘umrah, but it is haraam for her to circumambulate the Ka’bah until after her menses ends. The Prophet (peace and blessings of Allaah be upon him) said to ‘Aa’ishah (may Allaah be pleased with her) when she got her menses before entering Makkah: “Do everything that the pilgrim does but do not circumambulate the House until you become pure (i.e., your menses ends). Agreed upon.
It is proven in Saheeh al-Bukhaari that when she became pure, she circumambulated the Ka’bah and did saa’i between al-Safa and al-Marwah. This indicates that if a woman gets her menses before doing tawaaf, she should not do tawaaf and saa’i until she becomes pure.
Based on this, what you wife must do is wait until she becomes pure, and then circumambulate the Ka’bah and do saa’i between al-Safa and al-Marwah, then cut her hair. Then she will have completed her ‘umrah. And she does not have to offer a ransom for having gotten her menses when she was in ihraam.
See also the answer to question no. 40608.
And Allaah knows best.